Shifted training sequences in a communications system

ABSTRACT

Embodiments of the present invention can be used to select a training sequence used by a base station and a user terminal for communications. In one embodiment, selecting the training sequence to use includes first selecting a training sequence from a set of training sequences. Then, a shift indicator is received, the shift indicator indicating a number of symbols the training sequence is to be shifted. A shifted training sequence is generated by shifting the selected training sequence by the number indicated by the received shift indicator, and the shifted training sequence is used for communication with a first transceiver on a communications channel. In another embodiment, a shift indicator indicating a number of symbols a training sequence is to be shifted is first selected, and then used to generate a shifted training sequence by shifting the training sequence by the number of symbols indicated by the selected shift indicator. The shifted training sequence is then used for communicating with a transceiver on a communications channel.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention applies to the field of communications systemsand, in particular, to training sequences and training signals.

2. Description of the Prior Art

Some communications systems, such as cellular voice and datacommunications systems, have several base stations in differentlocations available for use by mobile or fixed user terminals, such ascellular telephones or wireless web devices. Each base stationcommunicates with a user terminal using a communications channel. Forexample, a communications channel may consist of a time slot in a TDMA(Time Division Multiple Access) frame on a physical carrier frequency. ATDMA frame may contain, for example, three uplink receive time slotsfollowed by three downlink transmit time slots, or vice-versa. The timeslots may be used to transmit communication bursts, or they may bedelineated on a continuous signal.

A physical carrier frequency may be a 625 kHz band around a centralfrequency, such as 800 MHz or 1.9 GHz. Thus, a base station transmits toa given user terminal, for example, on the second transmit and receivetime slots on this carrier frequency in a given frame. Furthermore, thecommunications channel may be organized using common duplexingtechniques, such as FDD (Frequency Division Duplex) and TDD (TimeDivision Duplex), and common multiple access techniques such as FDMA(Frequency Division Multiple Access) and CDMA (Code Division MultipleAccess). The channel may further be organized according to a hoppingfunction indicating alternating resources over time.

The communications channel can be used for sending signals thatcommunicate information, such as user data and control data. Thecommunications channel may also be used for sending signals that areknown at the receiver. Such signals are known as training or pilotsignals. A training signal can be generated in many ways, such assending a known symbol sequence, typically called a training sequence.In portions of the description below, the terms training signal andtraining sequence may be used interchangeably.

Training signals and training sequences can be used for measuringchannel parameters and characteristics, such as SNR (signal to noiseratio), spatial parameters, timing, and frequency offset. They can alsobe used for synchronizing symbols and frames, calibrating transceiversand equalizers, and calculating spatial and temporal filter weights. Onereason training sequences are useful, is that the received signal can becompared with the known sent signal, e.g., the known training sequence.Training sequences are used for “training,” which generally meansperforming some operation including comparing a received signal to aknown reference signal. Thus, the above example uses of training signalsand training sequences all constitute training.

A well-designed family of training sequences may have some useful ordesirable properties. For example, one useful property that a family oftraining sequences can have is that two different training sequencesfrom the family are as different as possible for all or most shifts.Another useful property that a family of training sequences can have isthat a delayed, or shifted, training sequence in the family should bedifferent from the same training sequence without shift. The firstproperty is enhanced if the absolute value of the cross-correlations ofany two training sequences is kept small. The second property isenhanced if the out-of-phase auto-correlations of the training sequencesare kept small. Different systems may be enhanced by using differenttradeoffs between various properties of training sequences, includingthe size of the sequences and the correlation properties describedabove.

BRIEF SUMMARY OF THE INVENTION

Embodiments of the present invention can be used to select a trainingsequence used by a base station and a user terminal for communications.In one embodiment, selecting the training sequence to use includes firstselecting a training sequence from a set of training sequences. Then, ashift indicator is received, the shift indicator indicating a number ofsymbols the training sequence is to be shifted. A shifted trainingsequence is generated by shifting the selected training sequence by thenumber indicated by the received shift indicator, and the shiftedtraining sequence is used for communication with a first transceiver ona communications channel. In another embodiment, a shift indicatorindicating a number of symbols a training sequence is to be shifted isfirst selected, and then used to generate a shifted training sequence byshifting the training sequence by the number of symbols indicated by theselected shift indicator. The shifted training sequence is then used forcommunicating with a transceiver on a communications channel.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings in which likereference numerals refer to similar elements and in which:

FIG. 1 is a flow chart of selecting a training sequence for useaccording to one embodiment of the invention.

FIG. 2 is a flow chart of shifting a core training sequence according toanother embodiment of the invention.

FIG. 3 is a flow chart of generating a core training sequence to beallocated to a base station according to one embodiment of theinvention.

FIG. 4 is a simplified block diagram of a base station on which anembodiment of the invention can be implemented; and

FIG. 5 is a simplified block diagram of a remote terminal on which anembodiment of the invention can be implemented.

DETAILED DESCRIPTION OF THE INVENTION

According to one embodiment of the invention, a base station uses acyclically shifted version of its core training sequence for thetraining segment of signals sent to or received from a particular userterminal. The user terminal is assigned to a spatial channel, and thespatial channel number determines the magnitude of the cyclic shift, sothat each user terminal sharing a conventional channel to communicatewith the base station uses a different shifted version of one coretraining sequence.

Training Sequence Selection

One embodiment of the present invention can be understood with referenceto FIG. 1. FIG. 1 provides a flow chart for selecting a trainingsequence to compare to a received training segment. In the embodimentdescribed with reference to FIG. 1, a user terminal performs theprocess. According to FIG. 1, the user terminal first selects 102 a coretraining sequence, and receives 104 a shift indicator from a basestation that indicates the number of symbols by which the core trainingsequence will be shifted. Then, the user terminal generates 106 ashifted training by performing the shift indicated by the shiftindicator, and uses the shifted training sequence to communicate 108with the base station.

FIG. 1 is now described in more detail. First, the user terminal selects102 a core training sequence from a set of core training sequences. Theset of core training sequences may be the core training sequencesdescribed below with respect to FIG. 3, or they may be any other set ofcore training sequences used by base stations of a communicationssystem. In one embodiment, the user terminal selects the core trainingsequence based on an identifier of the base station with which the userterminal is communicating.

For example, the user terminal can listen to a Broadcast Channel (BCH)containing a Base Station Color Code (BSCC) and select a core trainingsequence associated with the BSCC in the network. The BSCCs are used toeffectively partition resources, such as physical carriers and trainingsequences. In one embodiment, there are 32 BSCC used by the system, andalso 32 core training sequences to assign to the base stations. In thiscase, and each base station in the system can be assigned one of 32BSCCs. Then, each base station can be assigned the core trainingsequence that corresponds with its BSCC. If there are more than 32 basestations in the network, which is likely in a real-life system, a BSCCdoes not uniquely identify the base station that it is assigned to.However, the BSCC of a base station does uniquely identify the trainingsequence used by the base station since there is a one-to-onecorrespondence between BSCCs and core training sequences. Thus, once auser terminal learns the BSCC of a base station prior to or duringregistration, the user terminal can select the core training sequenceused by the base station.

Furthermore, the user terminal receives 104 a shift indicator from thebase station. The shift indicator indicates the amount, i.e., the numberof symbols, by which the selected core training sequence should beshifted by the user terminal. The base station also shifts its coretraining sequence prior to including it in a signal to be sent to theuser terminal, thus the shift indicator is sent from the base station toinform the user terminal of the magnitude of the shift. The shifting maybe cyclic in order to keep the length of the training sequence constant.For example, cyclically shifting the binary symbol sequence 001101100010to the left by two symbols results in the shifted sequence 110110001000.Of course, changing the starting point from the first position to thethird and reading left to right in a loop has the same effect. The shiftindicator can also be applied to the training signal. For example, ifthe above sequence is modulated such that each symbol takes up 2 μs onthe burst or waveform to be sent, then delaying or lagging the signal by4 μs has the same effect as shifting the above training sequence by twosymbols. If the sequence is repeated, then the lag may be identical to acyclic shift.

In one embodiment, the “spatial channel assignment,” or spatial channelnumber, of the user terminal determines the shift indicator. Asexplained above, a communications channel, also known as a conventionalchannel, can be a frequency band and a time slot in an FDMA/TDMA system,or a frequency band and a spreading code in a CDMA system. However,using adaptive antenna arrays and SDMA (Spatial Division MultipleAccess) strategies, two or more user terminals can share a singleconventional communications channel for communications with a basestation. These new “channels” created using SDMA can be called “spatialchannels.”

Two user terminals using the same conventional communications channelwithin a system can be called “co-channel” user terminals. One userterminal is sometimes also referred to as a “co-channel interferer” tothe other user terminal. This term is typically used when two co-channeluser terminals are communicating with different base stations. When twoco-channel terminals communicate with the same base station, they areusing different spatial channels. Such terminals are sometimes referredto as “co-spatial” user terminals. Such user terminals are servicedusing SDMA to distinguish the different terminals using the differentspatial channels constructed from the shared communications channel. Thenumber of co-channel user terminals that can share a communicationschannel to communicate with the same base station on different spatialchannels can vary.

In one embodiment, a maximum of five co-channel terminals can beserviced by one base station on one conventional communications channel.That is, each communications channel can support up to five spatialchannels. In this case, the “spatial channel assignment” of a userterminal can be any designation used by the base station to distinguishthe user terminal from the other co-channel user terminals the basestation is servicing. For example, if the user terminal arrives at thebase station at a time when there are already three other terminalssharing the channel to be assigned to the user terminal—these otherterminals designated as spatial channel 1, spatial channel 2, andspatial channel 3, respectively—then the newly arrived user terminal canbe designated as either spatial channel 4 or 5. If the user terminal isdesignated as spatial channel 4, and at some time in the future the userterminal designated as spatial channel 2 leaves the base station, aterminal arriving at this time could be designated as spatial channel 2or 5. Thus, the spatial channel number can be used to distinguish theco-channel user terminals serviced by one base station.

In one embodiment, the spatial channel assignment directly determinesthe shift indicator. For example, if a user terminal is designatedspatial channel 1, this may mean that the shift indicator indicates a0-symbol shift, i.e., no shift at all. Similarly, spatial channels2,3,4, and 5 may directly correspond with a 5,10,15, and 20-symbolshift, respectively. Alternately, to improve shift distances, spatialchannels 2,3,4, and 5 may directly correspond with a 10,20,5, and15-symbol shift, respectively. In this embodiment, the spatial channelassignment is, in effect, the shift indicator, since it uniquely definesthe number of symbols to be shifted. Thus, in this embodiment, receivinga shift indicator is identical to receiving a spatial channel assignmentor spatial channel number from the base station.

The precise magnitudes of the various shifts employed can vary dependingon the size of the core sequences to be shifted. In one embodiment, theshifts also depend on the number of user terminal sharing acommunications channel, i.e., the number of co-channel terminalsserviced by the base station. For example, if the there are twoco-channel terminals sharing a conventional channel—assuming a sequencelength of 64—the first user terminal may use an unshifted core sequencewhile the second terminal may use a core sequence shifted by 30, for alarge separation between the two shifted sequences. If a third userterminal is assigned a spatial channel on the same conventional channel,thus resulting in three co-channel user terminals being serviced by thebase station on this conventional channel, then the first user terminalmay continue to use the unshifted core sequence, while the second andthird terminals may shift the core sequence by 20 and 40 respectively,to maintain large shift differences. Various other ways are possible toallocate shifts.

After the shift indicator is received and the number of symbols to beshifted is known, the user terminal generates 106 a shifted trainingsequence by performing the shift indicated by the shift indicator. Thedirection of the shift may be implied, or it may be contained in theshift indicator. In one embodiment, the number contained in the shiftindicator is the number of symbols by which the selected core trainingsequence is to be shifted to the left. In one embodiment, the shiftingis cyclic, that is, the front symbols are placed at the back of thesequence.

There are numerous ways of executing the shift to generate the shiftedtraining sequence. An example above showed that cyclically shifting thebinary symbol sequence 001101100010 to the left by two symbols resultsin the shifted sequence 110110001000. Training sequences can be shiftedin the same manner. To arrive at this shifted sequence, a user terminalcan actually shift the core training sequence stored in memory. Inanother embodiment, the user terminal can start the sequence in thethird position, i.e., with the first 1, and read cyclically. In yetanother embodiment, the user terminal can store the sequence twice in arow, i.e., as 001101100011000110110000. Then, starting with the thirdposition, and taking the 12 subsequent symbols results in the shiftedsequence. The number of symbols repeated at the end of the sequence neednot exceed the maximum shift.

After the shifted training sequence is generated, it is used 108 forcommunication on the communications channel with the base station. Inone embodiment, the base station includes a training signal based on theshifted training sequence in this sent signal. That is, for example, thebase station sends a burst including the shifted training sequence as atraining segment. Since, as discussed above, the base station uses ashift that is coordinated with the shift done by the user terminal, theshifted training sequence sent from the base station will match theshifted training sequence generated by the user terminal. After thesignal is received, the shifted training sequence can be used fortraining in any traditional way, including for measuring channel andspatial parameters, synchronization, calibration, or the calculation ofspatial and temporal filter weights. Also, in one embodiment, the userterminal sends a signal to the base station containing the shiftedtraining sequence for a training segment. The base station may use thistraining segment for training in manner, including the operationsdescribed above.

One embodiment of the present invention can be understood with referenceto FIG. 2. FIG. 2 provides a flow chart of selecting a training sequenceto include in a signal to be sent by a base station. According to FIG.2, the base station first selects 202 a shift indicator, and generates204 a shifted training by performing the shift indicated by the shiftindicator. Then the base station communicates 206 with a user terminalusing the shifted training sequence.

FIG. 2 is now described in more detail. First, the base station selects202 a shift indicator. The shift indicator is to be used, as above, toindicate the number of symbols a core training sequence is to beshifted. Since the selected shift indicator is communicated to theappropriate user terminal, the description related to receiving 102 theshift indicator in FIG. 1 is applicable to selecting 202 the shiftindicator in FIG. 2. That is, in one embodiment, the spatial channelnumber that the base station assigns to the user terminal with which thebase station will use the training sequence directly determines theshift indicator. As explained above, if, for example, the base stationassigns spatial channel 3 to a user terminal, the base station hasselected a shift indicator indicating a 10-symbol shift. Thus, in thisembodiment, selecting a shift indicator is identical to assigning aspatial channel to a user terminal communicating with the base station.

After the shift indicator is selected, the base station generates 204the shifted training sequence by shifting the core training sequence ofthe base station in the manner indicated by the shift indicator. Usingthe example above, if the base station has assigned a user terminal tospatial channel 3, it shifts its core sequence 10 symbols to the left.In one embodiment, the base stations of the communications system eachhave one to generating sequence, thus the base station need not select acore training sequence prior to generating the shifted training sequencebecause it only has one. In other embodiments, the base station may havemultiple core sequences to choose from. Various practical ways ofperforming the shifting of the core training sequence have beendescribed with reference to FIG. 1 above.

When the shifted training sequence has been generated, it is used forcommunicating 206 with the appropriate user terminal. That is, the basestation may send or receive a signal, such as a burst, to the userterminal including the shifted training sequence. In other words, theshifted training signal can be used to generate a training or pilotsignal for the burst to be sent. Phrased yet another way, the shiftedtraining sequence can be inserted for the training segment of the signalabout to be sent.

DEMONSTRATIVE EXAMPLE

The following example may further clarify the embodiments of theinvention described above. The following example is a specificembodiment of the invention including many specific details set forth toillustrate. Other embodiments of the invention are not limited to any ofthe following details.

In this example communications system, each base station is assigned onecore training sequence from a set of core training sequences. The basestations are each assigned a physical carrier set of 8 physical carriersand use three uplink/downlink TDMA time slots per frame for a total of24 conventional channels. The base stations can service up to five userterminals on each conventional channel using SDMA strategies. In otherwords, a base station can split a conventional channel into up to fivespatial channels, and is thus able to service 120 user terminalssimultaneously on the 24 conventional channels. In different systems,there may be different numbers of physical carriers, time slots, andspatial channels per conventional channel.

A base station in the system uses its assigned core sequence for theterminals communicating on different conventional channels, but usesdifferent cyclically shifted versions of its core sequence for theco-channel user terminals communicating with the base station that sharea conventional channel. Thus, two terminals communicating usingdifferent physical carriers or time slots, but the same spatial channelnumber, use the same version of the core sequence. However, twoterminals communicating using the same physical carrier and time slot,i.e., the same conventional channel, but different spatial channelnumbers use different shifted versions of the core training sequence.Because of this, each base station only needs to store one core trainingsequence.

Two major sources of interference experienced by user terminals in thisexample system are co-channel interference from other user terminalsusing the same conventional channel to communicate with other basestations, and interference from the co-channel user terminals using thesame conventional channel to communicate with the same base station.Since the co-channel user terminals that communicate with the same basestation are physically closer than the co-channel interferers fromterminals at other base stations, this interference is more severe.Therefore, in this example, it is more important that the shiftedversions of a core training sequence be more differentiated than thecore training sequences themselves. That is, it is more important thatthe core training sequences have low out-of-phase auto-correlations thanit is that they have low cross-correlations. Therefore, the coresequences are selected or designed so that they have these desiredproperties.

In the present example, there are 32 core training sequences, and 32Base Station Color Codes (BSCC), one BSCC corresponding with each coretraining sequence. Each base station is assigned a non-unique BSCC. Whenpossible, two base stations with the same BSCC are not locatedphysically near one another. Each base station stores only the coretraining sequence corresponding to its BSCC. Each user terminal storesall 32 core sequences. For example, each user terminal stores a lookuptable with 32 rows, with each row representing a core sequence and therow number corresponding to the BSCCs.

In this example, when a user terminal arrives at a base station, theuser terminal tunes to a Broadcast Channel (BCH) that broadcastsinformation about the system and the base station, including the BSCC ofthe particular base station broadcasting on the BCH. Duringregistration, the base station assigns the user terminal to aconventional channel that the user terminal may share with other userterminals using SDMA. To help keep these co-channel terminals distinct,the base station assigns a spatial channel number to the registered userterminal. The number is merely an index, and can be anything that can beused by the base station to uniquely distinguish the user terminal fromits co-channel terminals at the base station.

After the base station assigns the spatial channel number to the newlyarrived user terminal and communicates the spatial channel number to theuser terminal, both the base station and the user terminal know thetraining sequence to use. The base station will include as a trainingsequence in signals sent to the user terminal a shifted version of thecore sequence, the shift indicated by the spatial channel number.Conversely, the user terminal will expect to receive as a trainingsequence in signals sent from the base station a shifted version of thecore sequence corresponding with the BSCC of the base station, the shiftindicated by the spatial channel number.

In a specific demonstrative example, user terminals A, B, and C (UTA,UTB, UTC) arrive at the base station with BSCC 16 (BS16). BS16 storescore training sequence 16 (TS16), where TS16 is the 16 bit binarysequence 1011011110101001. BS16 assigns UTA to conventional channel 5,spatial channel 3, UTB to conventional channel 8, spatial channel 3, andUTC to conventional channel 8, spatial channel 1 respectively. BS16sends a signal including a 16 bit training sequence to UTA with a12-symbol cyclic left-shift indicated by spatial channel 3. Thus, thetraining sequence sent to UTA is 1001101101111010. Since UTB is alsoassigned a spatial channel number of 3, the same training sequence1001101101111010 is included in signals sent to UTB. However, BS16 sendsa signal including a 16 bit training sequence to UTC with a 4-symbolcyclic left-shift indicated by spatial channel 1. Thus, the trainingsequence sent to UTC is 0111101010011011. The user terminals expect toreceive the correct sequences, because they look up core sequence TS16after learning that the BSCC of BS16 is 16, and shift TS16 identicallyto the base station based on the spatial channel number assignment ofeach user terminal.

Core Training Sequences

As mentioned above, in some embodiments of the present invention, it isdesirable that the core sequences assigned to the base stations of thecommunications system have certain correlation properties. In oneembodiment, a base station uses different shifted or delayed versions ofa core sequence as a training sequence for different co-channel userterminals communicating with the base station. Since the interferencefrom these co-channel terminals may be a significant source ofinterference, in one embodiment, the worst-case absolute value of theout-of-phase auto-correlation of each of the core sequences is keptbelow a threshold. In one embodiment, the out-of-phase auto-correlationcan be defined mathematically by:

$\begin{matrix}{{R_{k,k}(\tau)} = {\frac{1}{N}{\sum\limits_{t = 0}^{N - 1}\;{{S_{k}^{*}(t)} \cdot {S_{k}( {t + \tau} )}}}}} & (1)\end{matrix}$

-   -   where N is the length of the core training sequence S, i.e., S        has N symbols,        -   S(t) is a symbol in S with index t, such that 0≦t≦N-1,        -   S*(t) is the complex conjugate of the symbol S(t),        -   τ is the shift, delay, or lag of the sequence,        -   and, in the term S(t+♯), the addition is performed modulo N.

For example, the autocorrelation of sequence S_(k)=[a₀,a₁,a₂,a₃]delayed, i.e. shifted left, by 1 isR_(k, k)(1)=¼(a₀*·a₁+a₁*·a₂+a₂*·a₃+a₃*·a₀) according to Equation 1. Thesymbols a₀-a₃ can be complex numbers representing constellation pointsin a modulation scheme. For example, using a BPSK modulation scheme thatmaps 0 to −1 and 1 to 1, the bit-sequence 0100 is represented by thesymbol sequence [−1,1,−1,−1]. Similarly, using a QPSK modulation schemethat maps “00” to 1, “01” to j, “11” to −1, and “10” to −j, where j isthe imaginary component of a complex number (the square root of −1), thebit-sequence 00101110 is represented by the symbol sequence[1,−j,−1,−j]. Thus, keeping the out-of-phase auto-correlation of a coretraining sequence below a threshold may be done by ensuring thatEquation 1 results in a number below the threshold for all, or most,shift values for τ.

Furthermore, in one embodiment, each base station is assigned one coretraining sequence from the set of core training sequences. Sinceco-channel interference may also be a significant source ofinterference, in one embodiment, the cross-correlation of all, or most,of the core sequences is also kept below a threshold. In one embodiment,the cross-correlation can be defined mathematically by:

$\begin{matrix}{{R_{k,j}(\tau)} = {\frac{1}{N}{\sum\limits_{t = 0}^{N - 1}\;{{S_{k}^{*}(t)} \cdot {S_{j}( {t - \tau} )}}}}} & (2)\end{matrix}$

-   -   where N is the length of the core training sequence S, i.e., S        has N symbols,        -   S(t) is a symbol in S with index t, such that 0≦t≦N-1,        -   S_(k) and S_(j), are two different core training sequences,        -   S*(t) is the complex conjugate of the symbol S(t),        -   τ is the shift, delay, or lag of a sequence,        -   k does not equal j,        -   and, in the term S(t+τ), the addition is performed modulo N.    -   a. For example, the cross correlation of core training sequence        S_(k)=[a0,a1,a₂,a₃] with another core training sequence        Sj=[b₀,b₁,b₂,b₃] delayed by 1 is:        R_(k,j)(1)=¼(a₀*·b₁+a₁*·b₂+a₂*·b₃+a₃*·b₀) according to        Equation 2. Thus, keeping the cross-correlation of the core        training sequences below a threshold may be done by ensuring        that Equation 2 results in a number below the threshold for all,        or most, shift values for τ, and core training sequence pairs        S_(k) and S_(j).    -   b. In one embodiment, the interference for a user terminal from        co-channel user terminals at the same base station is more        severe than the co-channel interference from terminals at other        base stations. In this embodiment, it is more important to        minimize the out-of-phase auto-correlations than the        cross-correlations. Thus, the threshold for the out-of-phase        auto correlations may be lower than the threshold for the        cross-correlations. For example, the threshold for the        worst-case out-of-phase autocorrelation may be 0.125, while the        threshold for the worst-case cross-correlation may be 0.25.        Other thresholds may be used depending on the requirements of        specific systems.    -   c. Various known sequences exist whose mathematical descriptions        result in some desirable correlation properties. Some of these        sequences include Gold, Kasami, and Kerdock family of sequences.        However, these sequences do not satisfy all constraints,        including length, number, and correlation thresholds of some        practical communications systems.    -   d. One embodiment of the present invention can be understood        with reference to FIG. 3. FIG. 3 provides a flow chart of        generating a core training sequence to be allocated to a base        station in the radio communication system. According to FIG. 3,        an initial seed sequence is selected 302 and used to generate        304 a family of sequences from the seed sequence. Then the        family is reduced to generate 306 a reduced family from which a        core training sequence is selected 308.    -   e. FIG. 3 is now described in more detail. First, an initial        sequence is selected 302 from an initial set of sequences. This        initial set may have some desirable correlation properties, and        may be a known sequence family, such as the sequence families        mentioned above, or a set generated by a computer search. The        selection of the initial sequence may be at random. In one        embodiment, the process described with reference to FIG. 3 is        repeated for all sequences in the initial set, thus, all        sequences in the initial set are eventually selected.

After the initial sequence is selected, it may be used as a seedsequence for generating 304 a family of sequences by insertingadditional symbols into the initial seed sequence. This family can besaid to be “descended” from the initial seed sequence. In oneembodiment, to keep the sequences in this family of equal length, thenumber of additional symbols inserted is constant for each insertion. Inone embodiment, the family may be generated by consecutively insertingevery possible sequence of a given number of symbols between everysymbol of the initial sequence.

Following is a short binary sequence example to illustrate thisembodiment. The initial sequence selected is 0110 and the number ofadditional symbols to be inserted is two. Then, all the possiblesupplemental sequences of length two are 00, 01, 10, and 11. Thepossible places of insertion into the initial sequence, i.e., the threeinsertion points indicated by ^, are 0^1^1^0. There are four possiblesupplemental sequences to be inserted at three possible insertionpoints, resulting in a family of 12 sequences of length six generatedfrom, i.e. descended from, the initial sequence. In this example, thosesequences are:

000110 001110 010110 011110 010010 010110 011010 011110 011000 011010011100 011110.With such short initial sequence, some resulting sequences are repeated.Repeated sequences are possible even when starting with longer initialsequences, and may be discarded. The above family of sequencesdemonstrates the concept of inserting supplemental sequences atinsertion points. Many other ways of inserting additional symbols arepossible.

After the family of sequences is generated from the selected initialsequence, a reduced family is generated 306 by eliminating somesequences from the family. One elimination criterion may be the maximumvalue of absolute out-of-phase auto-correlation. For example, anysequence in the family with a worst-case out-of-phase auto-correlationabove a threshold is eliminated. This threshold may be 0.125. Otherthresholds may be used depending on the specific requirements of thesystem the core training sequences are being generated for.

Another elimination criterion may be the value of absolute out-of-phaseauto-correlation for certain lags, i.e., shifts or delays. For example,any sequence in the family With a worst-case out-of-phaseauto-correlation for lags (τ) 1-5 above a second threshold is alsoeliminated from the family. This threshold can be lower than the firstthreshold to eliminate additional sequences. For example, the set oflags to choose τ from may be [0-3] and the second threshold may be 0.05.Other thresholds may be used depending on the specific requirements ofthe system the core training sequences are being generated for. Thistest may be repeated several times with different sets of lags anddifferent thresholds.

Yet another elimination criterion may be the absolute value of the meanof the symbols of the sequences. In one embodiment, any sequence with anabsolute value mean above some threshold is eliminated. That is, themean of the symbols, which are complex numbers, of a sequence iscalculated, resulting in a complex number. Then, the norm or absolutevalue of this mean, which is generally a real number, is compared to athreshold. This threshold may be 0.10. Other thresholds may be useddepending on the specific requirements of the system the core trainingsequences are being generated for. Numerous other elimination criteriamay be used in combination with, or instead of, the elimination criteriadiscussed above.

After the reduced family is generated, that is, after the eliminationcriteria have been applied, a sequence is selected 308 from the reducedfamily to be assigned to a base station in the radio communicationsnetwork as a core training sequence. As discussed above, in oneembodiment, the cross-correlations of the core training sequences arebelow a threshold. Since the sequences in the reduced family descendfrom the same initial seed sequence, their cross-correlations may not below enough. However, sequences from different reduced families generatedfrom different initial sequences may have better cross-correlationproperties. This may be especially true if the initial set of sequenceshad good cross-correlation properties. Accordingly, in one embodiment,each core training sequence to be assigned to a base station is selectedfrom a different reduced family descendant from a different initial seedsequence.

For example, if there are 32 BSCCs in a system, then the system needs 32core training sequences, one for each color code. In that case, 32 (ormore) reduced families of sequences can be generated based on a set of32 (or more) initial sequences according to a process described withreference to FIG. 3. Then, in this embodiment, one sequence is chosenfrom each reduced family in such a manner that these sequences havecross-correlations below a threshold, or that these sequences have thelowest possible cross-correlations. There are many ways of selecting asequence from each reduced family to achieve these results.

For example, this selection process can begin by selecting a sequencefrom each reduced family at random, and determining one or moreworst-case pairs, that is, those sequence pairs with the highestcross-correlations, among these sequences. Then, one sequence in each ofthe worst-case pairs can be discarded and replaced with another randomlyselected sequence from the reduced family that the discarded sequencewas a member of. Now, new worst-case pairs can be determined, and thisprocess can be iteratively repeated until the desired cross-correlationsare achieved. The resulting 32 sequences can be designated the 32 coretraining sequences for the system.

After the core training sequences have been selected from knownsequences, collected, or generated by some process, such as the processdescribed with reference to FIG. 3, they can be stored in the basestations and user terminals of the radio communications system. The coretraining sequences may be stored as mathematical descriptions. However,some core sequences may be impractical or impossible to store asmathematical descriptions. Thus, in one embodiment, a core trainingsequence, or at least one period of the core training sequence, isstored in memory, such as a memory on a base station like DSP 31 in FIG.4, as a sequence of symbols. In one embodiment, each base station hasone core training sequence assigned to it based on the BSCC of the basestation. Thus, only one core training sequence is stored. The basestation can use this core training sequence, and shifted versions ofthis core training sequence, as described with reference to FIG. 2above.

Since user terminals can be handed off between base stations, in oneembodiment, the user terminals in the system store all of the coretraining sequences in a memory, such as the memory in CPU 68 in FIG. 5.The core training sequences may be stored in a lookup table, with eachcore training sequence indexed by a BSCC. The user terminals can usethese core training sequences, and shifted versions of these coretraining sequences, as described with reference to FIG. 1 above.

Base Station Structure

The present invention relates to wireless communication systems and maybe a fixed-access or mobile-access wireless network using spatialdivision multiple access (SDMA) technology in combination with multipleaccess systems, such as time division multiple access (TDMA), frequencydivision multiple access (FDMA) and code division multiple access(CDMA). Multiple access can be combined with frequency divisionduplexing (FDD) or time division duplexing (TDD). FIG. 4 shows anexample of a base station of a wireless communications system or networksuitable for implementing the present invention. The system or networkincludes a number of subscriber stations, also referred to as remoteterminals or user terminals, such as that shown in FIG. 5. The basestation may be connected to a wide area network (WAN) through its hostDSP 31 for providing any required data services and connections externalto the immediate wireless system. To support spatial diversity, aplurality of antennas 3 is used to form an array 4, for example fourantennas, although other numbers of antennas may be selected.

A set of spatial multiplexing weights for each subscriber station areapplied to the respective modulated signals to produce spatiallymultiplexed signals to be transmitted by the bank of four antennas. Thehost DSP 31 produces and maintains spatial signatures for eachsubscriber station for each conventional channel and calculates spatialmultiplexing and demultiplexing weights using received signalmeasurements. In this manner, the signals from the current activesubscriber stations, some of which may be active on the sameconventional channel, are separated and interference and noisesuppressed. When communicating from the base station to the subscriberstations, an optimized multi-lobe antenna radiation pattern tailored tothe current active subscriber station connections and interferencesituation is created. Suitable smart antenna technologies for achievingsuch a spatially directed beam are described, for example, in U.S. Pat.Nos. 5,828,658, issued Oct. 27, 1998 to Ottersten et al. and 5,642,353,issued Jun. 24, 1997 to Roy, III et al. The channels used may bepartitioned in any manner. In one embodiment the channels used may bepartitioned as defined in the GSM (Global System for MobileCommunications) air interface, or any other time division air interfaceprotocol, such as Digital Cellular, PCS (Personal Communication System),PHS (Personal Handyphone System) or WLL (Wireless Local Loop).Alternatively, continuous analog or CDMA channels can be used.

The outputs of the antennas are connected to a duplexer switch 7, whichin a TDD embodiment, may be a time switch. Two possible implementationsof the duplexer switch are as a frequency duplexer in a frequencydivision duplex (FDD) system, and as a time switch in a time divisionduplex (TDD) system. When receiving, the antenna outputs are connectedvia the duplexer switch to a receiver 5, and are converted down inanalog by RF receiver (“RX”) modules 5 from the carrier frequency to anFM intermediate frequency (“IF”). This signal then is digitized(sampled) by analog to digital converters (“ADCs”) 9. Finaldown-converting to baseband is carried out digitally. Digital filterscan be used to implement the down-converting and the digital filtering,the latter using finite impulse response (FIR) filtering techniques.This is shown as block 13. The invention can be adapted to suit a widevariety of RF and IF carrier frequencies and bands.

There are, in the present example, eight down-converted outputs fromeach antenna's digital filter 13, one per receive timeslot. Theparticular number of timeslots can be varied to suit network needs.While GSM uses eight uplink and eight downlink timeslots for each TDMAframe, desirable results can also be achieved with any number of TDMAtimeslots, for example three timeslots, for the uplink and downlink ineach frame. For each of the eight receive timeslots, the fourdown-converted outputs from the four antennas are fed to a digitalsignal processor (DSP) 31 (hereinafter “timeslot processor”) for furtherprocessing, including calibration, according to one aspect of thisinvention. Eight Motorola DSP56300 Family DSPs can be used as timeslotprocessors, one per receive timeslot. The timeslot processors 17 monitorthe received signal power and estimate the frequency offset and timealignment. They also determine smart antenna weights for each antennaelement. These are used in the SDMA scheme to determine a signal from aparticular remote user and to demodulate the determined signal.

The output of the timeslot processors 17 is demodulated burst data foreach of the eight receive timeslots. This data is sent to the host DSPprocessor 31 whose main function is to control all elements of thesystem and interface with the higher level processing, which is theprocessing which deals with what signals are required for communicationsin all the different control and service communication channels definedin the system's communication protocol. The host DSP 31 can be aMotorola DSP56300 Family DSP. In addition, timeslot processors send thedetermined receive weights for each user terminal to the host DSP 31.The host DSP 31 maintains state and timing information, receives uplinkburst data from the timeslot processors 17, and programs the timeslotprocessors 17. In addition it decrypts, descrambles, checks errorcorrecting code, and deconstructs bursts of the uplink signals, thenformats the uplink signals to be sent for higher level processing inother parts of the base station. Furthermore DSP 31 may include a memoryelement to store data, instructions, or hopping functions or sequences.Alternatively, the base station may have a separate memory element orhave access to an auxiliary memory element. With respect to the otherparts of the base station it formats service data and traffic data forfurther higher processing in the base station, receives downlinkmessages and traffic data from the other parts of the base station,processes the downlink bursts and formats and sends the downlink burststo a transmit controller/modulator, shown as 37.

The host DSP also manages programming of other components of the basestation including the transmit controller/modulator 37 and the RF timingcontroller shown as 33. The RF controller 33 reads and transmits powermonitoring and control values, controls the duplexer 7 and receivestiming parameters and other settings for each burst from the host DSP31.

The transmit controller/modulator 37, receives transmit data from thehost DSP 31. The transmit controller uses this data to produce analog IFoutputs which are sent to the RF transmitter (TX) modules 39.Specifically, the received data bits are converted into a complexmodulated signal, up-converted to an IF frequency, sampled, multipliedby transmit weights obtained from host DSP 31, and converted via digitalto analog converters (“DACs”) which are part of transmitcontroller/modulator 37 to analog transmit waveforms. The analogwaveforms are sent to the transmit modules 39. The transmit modules 39up-convert the signals to the transmission frequency and amplify thesignals. The amplified transmission signal outputs are sent to antennas3 via the duplexer/time switch 7.

User Terminal Structure

FIG. 5 depicts an example component arrangement in a remote terminalthat provides data or voice communication. The remote terminal's antenna45 is connected to a duplexer 46 to permit the antenna 45 to be used forboth transmission and reception. The antenna can be omni-directional ordirectional. For optimal performance, the antenna can be made up ofmultiple elements and employ spatial processing as discussed above forthe base station. In an alternate embodiment, separate receive andtransmit antennas are used eliminating the need for the duplexer 46. Inanother alternate embodiment, where time division duplexing is used, atransmit/receive (TR) switch can be used instead of a duplexer as iswell known in the art. The duplexer output 47 serves as input to areceiver 48. The receiver 48 produces a down-converted signal 49, whichis the input to a demodulator 51. A demodulated received sound or voicesignal 67 is input to a speaker 66.

The remote terminal has a corresponding transmit chain in which data orvoice to be transmitted is modulated in a modulator 57. The modulatedsignal to be transmitted 59, output by the modulator 57, is up-convertedand amplified by a transmitter 60, producing a transmitter output signal61. The transmitter output 61 is then input to the duplexer 46 fortransmission by the antenna 45.

The demodulated received data 52 is supplied to a remote terminalcentral processing unit 68 (CPU) as is received data before demodulation50. The remote terminal CPU 68 can be implemented with a standard DSP(digital signal processor) device such as a Motorola series 56300 FamilyDSP. This DSP can also perform the functions of the demodulator 51 andthe modulator 57. The remote terminal CPU 68 controls the receiverthrough line 63, the transmitter through line 62, the demodulatorthrough line 52 and the modulator through line 58. It also communicateswith a keyboard 53 through line 54 and a display 56 through line 55. Amicrophone 64 and speaker 66 are connected through the modulator 57 andthe demodulator 51 through lines 65 and 67, respectively for a voicecommunications remote terminal. In another embodiment, the microphoneand speaker are also in direct communication with the CPU to providevoice or data communications. Furthermore remote terminal CPU 68 mayalso include a memory element to store data, instructions, and hoppingfunctions or sequences. Alternatively, the remote terminal may have aseparate memory element or have access to an auxiliary memory element.

In one embodiment, the speaker 66, and the microphone 64 are replaced oraugmented by digital interfaces well-known in the art that allow data tobe transmitted to and from an external data processing device (forexample, a computer). In one embodiment, the remote terminal's CPU iscoupled to a standard digital interface such as a PCMCIA interface to anexternal computer and the display, keyboard, microphone and speaker area part of the external computer. The remote terminal's CPU 68communicates with these components through the digital interface and theexternal computer's controller. For data only communications, themicrophone and speaker can be deleted. For voice only communications,the keyboard and display can be deleted.

General Matters

In the description above, for the purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of the present invention. It will be apparent, however, toone skilled in the art that the present invention may be practicedwithout some of these specific details. In other instances, well-knownstructures and devices are shown in block diagram form.

The present invention includes various steps. The steps of the presentinvention may be performed by hardware components, such as those shownin FIGS. 4 and 5, or may be embodied in machine-executable instructions,which may be used to cause a general-purpose or special-purposeprocessor or logic circuits programmed with the instructions to performthe steps. Alternatively, the steps may be performed by a combination ofhardware and software. The steps have been described as being performedby either the base station or the user terminal. However, many of thesteps described as being performed by the base station may be performedby the user terminal and vice versa. Furthermore, the invention isequally applicable to systems in which terminals communicate with eachother without either one being designated as a base station, a userterminal, a remote terminal or a subscriber station. Thus, the presentinvention is equally applicable and useful in a peer-to-peer wirelessnetwork of communications devices using frequency hopping and spatialprocessing. These devices may be cellular phones, PDA's, laptopcomputers, or any other wireless devices. These devices may sometimes begenerally referred to as radios or transceivers.

In portions of the description above, the training sequence was sent bythe base station to the user terminal. However, embodiments of thepresent invention may be used on the uplink or the downlink by either abase station or a user terminal, or any other communications device thatis not designated as either, as, for example, in a Peer-to-Peer system.

Furthermore, in portions of the description above, operations such asselecting and shifting are performed on a training sequence. However,these operations may be performed at the signal level. In other words,shifting a training sequence by two symbols can be the same as shiftinga training signal by 4 μs.

Furthermore, in portions of the description above, various examplesequences are shown that have certain lengths, i.e., number of symbols.Sequences of other lengths are also discussed. However, embodiments ofthe present invention may be used with core training sequences, or anyother sequence, of any size.

Furthermore, embodiments of the present invention have been described inthe context of a wireless radio communications system. However,embodiments of the present invention may be applicable in anycommunications system, including wired landline systems, such as thetelephone system, digital subscriber lines (DSL), and cable television(CATV) system.

The present invention may be provided as a computer program product,which may include a machine-readable medium having stored thereoninstructions, which may be used to program a computer (or otherelectronic devices) to perform a process according to the presentinvention. The machine-readable medium may include, but is not limitedto, floppy diskettes, optical disks, CD-ROMs, and magneto-optical disks,ROMs, RAMs, EPROMs, EEPROMs, magnet or optical cards, flash memory, orother type of media/machine-readable medium suitable for storingelectronic instructions.

Many of the methods are described in their most basic form, but stepscan be added to or deleted from any of the methods and information canbe added or subtracted from any of the described messages withoutdeparting from the basic scope of the present invention. It will beapparent to those skilled in the art that many further modifications andadaptations can be made. The particular embodiments are not provided tolimit the invention but to illustrate it. The scope of the presentinvention is not to be determined by the specific examples providedabove but only by the claims below.

It should also be appreciated that reference throughout thisspecification to “one embodiment” or “an embodiment” means that aparticular feature may be included in the practice of the invention.Similarly, it should be appreciated that in the foregoing description ofexemplary embodiments of the invention, various features of theinvention are sometimes grouped together in a single embodiment, figure,or description thereof for the purpose of streamlining the disclosureand aiding in the understanding of one or more of the various inventiveaspects. This method of disclosure, however, is not to be interpreted asreflecting an intention that the claimed invention requires morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive aspects lie in less than allfeatures of a single foregoing disclosed embodiment. Thus, the claimsfollowing the Detailed Description are hereby expressly incorporatedinto this Detailed Description, with each claim standing on its own as aseparate embodiment of this invention.

1. A method performed by a communications device comprising: receivingan identification of a first transceiver over a wireless communicationschannel; selecting a core training sequence based on the receivedidentification; receiving a spatial channel assignment from the firsttransceiver; selecting a shift indicator using the spatial channelassignment, the shift indicator indicating a number of symbols that thecore training sequence stored in a memory of the communications deviceis to be shifted; generating a shifted training sequence by shifting thecore training sequence by the number of symbols indicated by theselected shift indicator, and communicating from a second transceiver ofthe communications device on the assigned communications channel usingthe shifted training sequence.
 2. The method of claim 1, whereincommunicating comprises sending a signal to the first transceiver, thesignal containing the shifted training sequence.
 3. The method of claim1, wherein communicating comprises receiving a signal from the secondtransceiver, the signal containing a received training sequencecorresponding to the shifted training sequence.
 4. The method of claim3, wherein communicating further comprises training by comparing thereceived training sequence with the shifted training sequence.
 5. Themethod of claim 4, wherein training comprises one or more of measuring achannel parameter of the assigned communications channel, measuring asignal to noise ratio (SNR), measuring a signal to interference andnoise ratio (SINR), estimating a spatial parameter, estimating a timingoffset of the communications channel, estimating a frequency offset ofthe communications channel, synchronizing symbols, synchronizing frames,calibrating a transceiver, calibrating an equalizer, and calculatingspatial and temporal filter weights.
 6. The method of claim 1, whereinreceiving an identification comprises receiving an identifier of thefirst transceiver to the second transceiver in a broadcast channel. 7.The method of claim 6, wherein the first transceiver comprises a basestation, the identifier of the first transceiver comprises a BaseStation Color Code (BSCC), and the training sequence comprises a coretraining sequence corresponding to the BSCC.
 8. The method of claim 1,further comprising: selecting a second shift indicator indicating adifferent number of symbols than the shift indicator; generating asecond shifted training sequence by cyclically shifting the trainingsequence by the number indicated by the second shift indicator;communicating with a third transceiver on the communications channelusing the second shifted training sequence.
 9. The method of claim 8,wherein communicating with the third transceiver comprises sending asignal containing the shifted training sequence to the secondtransceiver and sending a signal containing the second shifted trainingsequence to the third transceiver simultaneously on the samecommunications channel.
 10. The method of claim 8, wherein communicatingwith the third transceiver comprises receiving a signal containing theshifted training sequence from the second transceiver and receiving asignal containing the second shifted training sequence from the thirdtransceiver simultaneously on the same communications channel.
 11. Themethod of claim 1, wherein the training sequence has a maximumout-of-phase auto-correlation below a threshold.
 12. The method of claim8, wherein the correlation between the shifted training sequence and thesecond shifted training sequence is below a threshold.
 13. Acommunications device comprising: a processor to: receive anidentification of a first transceiver over a wireless communicationschannel; select a core training sequence based on the receivedidentification; receive a spatial channel assignment from the firsttransceiver; select a shift indicator using the spatial channelassignment, the shift indicator indicating a number of symbols that thecore training sequence is to be shifted; and generate a shifted trainingsequence by shifting the core training sequence by the number of symbolsindicated by the selected shift indicator; and a second transceiver tocommunicate with the first transceiver on the assigned communicationschannel using the shifted training sequence.
 14. The communicationsdevice of claim 13, wherein the second transceiver communicates with thefirst transceiver by sending a signal to the first transceiver, thesignal containing the shifted training sequence.
 15. The communicationsdevice of claim 13, wherein the second transceiver communicates with thefirst transceiver by receiving a signal from the first transceiver, thesignal containing a received training sequence corresponding to theshifted training sequence.
 16. The communications device of claim 15,wherein the processor uses the shifted training sequence for training bycomparing the received training sequence with the shifted trainingsequence.
 17. The communications device of claim 16, wherein trainingcomprises one or more of measuring a channel parameter of the assignedcommunications channel, measuring a signal to noise ratio (SNR),measuring a signal to interference and noise ratio (SINR), estimating aspatial parameter, estimating a timing offset of the communicationschannel, estimating a frequency offset of the communications Channel,synchronizing symbols, synchronizing frames, calibrating a transceiver,calibrating an equalizer, and calculating spatial and temporal filterweights.
 18. The communications device of claim 13, wherein the firsttransceiver sends an identifier of the communications device to thesecond transceiver.
 19. The communications device of claim 18, whereinthe first transceiver comprises a base station, the identifier of thefirst transceiver comprises a Base Station Color Code (BSCC), and thetraining sequence comprises a core training sequence corresponding tothe BSCC.
 20. The communications device of claim 13, wherein theprocessor: selects a second shift indicator indicating a differentnumber of symbols than the shift indicator; generates a second shiftedtraining sequence by cyclically shifting the training sequence by thenumber indicated by the second shift indicator; and wherein the firsttransceiver communicates with a second remote transceiver on thecommunications channel using the second shifted training sequence. 21.The communications device of claim 20, wherein the first transceiversends a signal containing the shifted training sequence to the secondtransceiver, and sends a signal containing the second shifted trainingsequence to the second remote transceiver simultaneously on the samecommunications channel.
 22. The communications device of claim 20,wherein the first transceiver receives a signal containing the shiftedtraining sequence from the second transceiver, and receives a signalcontaining the second shifted training sequence from the second remotetransceiver simultaneously on the same communications channel.
 23. Thecommunications device of claim 13, wherein the training sequence has amaximum out-of-phase auto-correlation below a threshold.
 24. Thecommunications device of claim 20, wherein the correlation between theshifted training sequence and the second shifted training sequence isbelow a threshold.
 25. The communications device of claim 20, whereinthe second transceiver and the second remote transceiver comprise userterminals, and the first transceiver comprises a base station.
 26. Amachine-readable medium having stored thereon data representinginstructions that, when executed by a processor, cause the processor toperform operations comprising: receiving an identification of a firsttransceiver over a wireless communications channel; selecting a coretraining sequence based on the received identification; receiving aspatial channel assignment from the first transceiver; selecting a shiftindicator using the spatial channel assignment, the shift indicatorindicating a number of symbols that the core training sequence stored ina memory of the communications device is to be shifted; generating ashifted training sequence by shifting the core training sequence by thenumber of symbols indicated by the selected shift indicator; andcommunicating from a second transceiver of the communications device onthe assigned communications channel using the shifted training sequence.27. The machine-readable medium of claim 26, wherein communicatingcomprises sending a signal from the second transceiver to the firsttransceiver, the signal containing the shifted training sequence. 28.The machine-readable medium of claim 26, wherein communicating comprisesreceiving a signal at the first transceiver from the second transceiver,the signal containing a received training sequence corresponding to theshifted training sequence.
 29. The machine-readable medium of claim 26,wherein the instructions further cause the processor to performoperations comprising: selecting a second shift indicator indicating adifferent number of symbols than the shift indicator; generating asecond shifted training sequence by cyclically shifting the trainingsequence by the number indicated by the second shift indicator;communicating with a third transceiver on the communications channelusing the second shifted training sequence.
 30. The machine-readablemedium of claim 29, wherein communicating with the third transceivercomprises sending a signal containing the shifted training sequence fromthe first transceiver to the second transceiver and sending a signalcontaining the second shifted training sequence from the firsttransceiver to the third transceiver simultaneously on the samecommunications channel.
 31. The machine-readable medium of claim 29,wherein communicating with the third transceiver comprises receiving asignal containing the shifted training sequence from the secondtransceiver at a first transceiver and receiving a signal containing thesecond shifted training sequence from the third transceiver at the firsttransceiver simultaneously on the same communications channel.
 32. Themachine-readable medium of claim 26, wherein the training sequence has amaximum out-of-phase auto-correlation below a threshold.
 33. Themachine-readable medium of claim 29, wherein the correlation between theshifted training sequence and the second shifted training sequence isbelow a threshold.